# If an article is sold for Rs.178 at a loss of 11%. What should be its selling price in order to earn a profit of 11%?

A. Rs.222.50

B. Rs.267

C. Rs.222

D. Rs.220

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**Hint:**First of all, find out the cost price of the article by using the given data and the formula \[{\text{C}}{\text{.P}} = \dfrac{{{\text{S}}{\text{.P}}}}{{100 - {\text{Loss% }}}} \times 100\]. Then find out the selling with a profit of 11% by using the formula \[{\text{S}}{\text{.P}} = \dfrac{{100 + {\text{Profit% }}}}{{100}} \times {\text{C}}{\text{.P}}\]. So, use this concept to reach the solution of the given problem.

__Complete step-by-step answer__:Given that the article is sold for Rs.178 at a loss of 11%.

So, selling price of article = Rs.178

Loss percent = 11%

We know that \[{\text{C}}{\text{.P}} = \dfrac{{{\text{S}}{\text{.P}}}}{{100 - {\text{Loss% }}}} \times 100\]

So, cost price of the article \[ = \dfrac{{178}}{{100 - 11}} \times 100 = \dfrac{{178}}{{89}} \times 100 = 2 \times 100 = {\text{Rs}}.200\]

Now, we have to find the selling price of the article in order to get a profit of 11%

We know that, \[{\text{S}}{\text{.P}} = \dfrac{{100 + {\text{Profit% }}}}{{100}} \times {\text{C}}{\text{.P}}\]

So, selling price of the article to have profit of 11% \[ = \dfrac{{100 + 11}}{{100}} \times 200\]

\[

= \dfrac{{111 \times 200}}{{100}} \\

= 111 \times 2 \\

= {\text{Rs}}{\text{.222}} \\

\]

Hence, to gain a profit of 11% the selling price should be Rs.222

**Thus, the correct option is C. Rs.222**

**Note**: There is a loss whenever the cost price of the article is greater than the selling price of the article. And there is a profit whenever the selling price of the article is greater than the cost price of the article.